Spectral computed tomography has received considerable interest in recent years since spectral measurements contain much richer information about the object of interest. In spectral computed tomography, we are interested in the energy channel-wise reconstructions of the object. However, such reconstructions suffer from low signal-to-noise ratio and share the challenges of conventional low-dose computed tomography such as ring artifacts. Ring artifacts arise from errors in the flat-field correction and can significantly degrade the quality of the reconstruction. We propose an extended flat-field model that exploits high correlation in the spectral flat-fields to reduce ring artifacts in the channel-wise reconstructions. The extended model relies on the assumption that the spectral flat-fields can be well-approximated by a low-rank matrix. Our proposed model works directly on the spectral flat-fields and can be combined with any existing reconstruction model, e.g., filtered back projection and iterative methods. The proposed model is validated on a neutron data set. The results show that our method successfully diminishes ring artifacts and improves the quality of the reconstructions. Moreover, the results indicate that our method is robust; it only needs a single spectral flat-field image, whereas existing methods need multiple spectral flat-field images to reach a similar level of ring reduction.

Chronic kidney diseases imply an ongoing need to remove toxins, with hemodialysis as the preferred treatment modality. We derive analytical expressions for phosphate clearance during dialysis, the single pass (SP) model corresponding to a standard clinical hemodialysis and the multi pass (MP) model, where dialysate is recycled and therefore makes a smaller clinical setting possible such as a transportable dialysis suitcase. For both cases we show that the convective contribution to the dialysate is negligible for the phosphate kinetics and derive simpler expressions. The SP and MP models are calibrated to clinical data of ten patients showing consistency between the models and provide estimates of the kinetic parameters. Immediately after dialysis a rebound effect is observed. We derive a simple formula describing this effect which is valid both posterior to SP or MP dialysis. The analytical formulas provide explanations to observations of previous clinical studies.

Hyperphosphatemia in patients with renal failure is associated with increased vascular calcification and mortality. Hemodialysis is a conventional treatment for patients with hyperphosphatemia. Phosphate kinetics during hemodialysis may be described by a diffusion process and modeled by ordinary differential equations. We propose a Bayesian model approach for estimating patient-specific parameters for phosphate kinetics during hemodialysis. The Bayesian approach allows us to both analyze the full parameter space using uncertainty quantification and to compare two types of hemodialysis treatments, the conventional single-pass and the novel multiple-pass treatment. We validate and test our models on synthetic and real data. The results show limited identifiability of the model parameters when only single-pass data are available, and that the Bayesian model greatly reduces the relative standard deviation compared to existing estimates. Moreover, the analysis of the Bayesian models reveal improved estimates with reduced uncertainty when considering consecutive sessions and multiple-pass treatment compared to single-pass treatment.

Reconstruction methods for computed tomography are often based on the assumption that the source intensity and the detector response are known and static. In practice, however, both are unknown and must be estimated. An estimate of the combined source intensity and detector response is typically obtained by acquiring a number of so-called flat-field measurements, but this approach is oblivious to intensity drift, e.g. due to source instabilities, vibrating beamline components, etc. Discrepancies between the estimated response and true response can lead to severe artifacts in the reconstruction, especially for dose- and/or time-limited experiments. We propose a new, extended reconstruction model that jointly estimates the reconstruction, the detector response, and the (possibly time-varying) source intensity. We demonstrate through simulated experiments that the proposed reconstruction model leads to reconstructions with significantly reduced artifacts.

Heterogeneity of stem cell clones provide a key ingredient in altered hematopoiesis and is of main interest in the study of predisease states as well as in the development of blood cancers such as chronic myeloid leukemia (CML) and the Philadelphia-negative myeloprofilerative neoplasms (MPNs). A mathematical model based on biological mechanisms and basic cell descriptors such as proliferation rates and apoptosis rates is suggested, connecting stem cell dynamics with mature blood cells and immune mediated feedback. The flexible approach allows for arbitrary numbers of mutated stem cell clones with perturbed properties. In particular, the stem cell niche provides a competition between wild type and mutated stem cells. Hence, the stem cell niche can mediate suppression of the wild type clones and up-regulation of one or more malignant clones. The model is parameterized using clinical data to show typical disease progression in several blood cancers and the hematological and molecular response to treatment. Intriguingly, occasional oscillatory cell counts observed during treatment of CML and MPNs can be explained by heterogeneous stem cell clone dynamics. Thus, the vital heterogeneous stem cell dynamics may be inferred from mathematical modeling in synergy with clinical data to elucidate hematopoiesis, blood cancers and the outcome of interventions.